Homocercal is a antonym of heterocercal.

Homocercal is a coordinate term of heterocercal.

In ichthyology terms the difference between heterocercal and homocercal

is that heterocercal is of a fish's tail, such that the vertebral column bends and extends upwards into the upper lobe of the tail, making it larger than the lower lobe; as in sharks, rays, and skates while homocercal is describing the symmetric tail of a fish that has two lobes extending from the end of the vertebral column.